Elliptic curve isogeny class 54684.2-a over number field Q(−3)\Q(\sqrt{-3})

• Base field: $\Q(\sqrt{-3})$
• Label: 2.0.3.1-54684.2-a
• Conductor: 54684.2
• Rank: $0$

Base field $\Q(\sqrt{-3})$

Generator $a$, with minimal polynomial $x^{2} - x + 1$; class number $1$.

Rank

Rank: $0$

Isogeny matrix

$\left(\begin{array}{rrrrr} 1 & 3 & 3 & 3 & 3 \\ 3 & 1 & 9 & 9 & 9 \\ 3 & 9 & 1 & 9 & 9 \\ 3 & 9 & 9 & 1 & 9 \\ 3 & 9 & 9 & 9 & 1 \end{array}\right)$

Isogeny graph

Elliptic curves in class 54684.2-a over $\Q(\sqrt{-3})$

Isogeny class 54684.2-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
54684.2-a1	$\bigl[1$ , $a$ , $0$ , $-367 a + 554$ , $2293 a + 3767\bigr]$
54684.2-a2	$\bigl[1$ , $a$ , $0$ , $3053 a - 4156$ , $6565 a - 58879\bigr]$
54684.2-a3	$\bigl[1$ , $a$ , $0$ , $83 a + 89$ , $-527 a + 752\bigr]$
54684.2-a4	$\bigl[1$ , $a$ , $0$ , $-7717 a - 3856$ , $397303 a - 10303\bigr]$
54684.2-a5	$\bigl[1$ , $a$ , $0$ , $-32887 a + 47339$ , $1679851 a + 2156108\bigr]$